$\"\"$

Length of the air duct is $\"\"$ .

Acute angle is $\"\"$ .

Depth of the shaft at small end is $\"\"$ .

Depth of the shaft at large end is $\"\"$ .

Redraw the diagram using above information.

$\"\"$

From the right angle triangle.

The length of opposite side is $\"\"$ .

The length of hypotenuse is $\"\"$ .

Trigonometric function : $\"\"$ .

$\"\"$

The length of the large end of the duct :

$\"\"$

Substitute $\"\"$ in above equation.

$\"\"$

The length of the large end of the duct is $\"\"$ .

$\"\"$

The length of the large end of the duct is $\"\"$ .